Abstract
This paper is a theoretical study on beam-to-column connections in steel square-tube columns. In the first, we assume that the boundaries of the square-tube cross section consist of two hypotrocoids. And then, we simplify beam-to-column connections to unti-symmetrical cantilevers and discuss bending of a steel squaretube cantilever by a force applied at the virtual free end of it. In the analysis of this problem, we apply Saint-Venant's flexure theory. We assume that normal stresses over a cross section are distributed in the same manner as in the case of pure bending, and assume that there are two shearing stress components and other three stress components are zero. With these assumptions, we can find the functions of shearing stress components which satisfy the equations of equilibrium, the boundary conditions and the compatibility equations. But, the wall thickness of the cross section the boundories of which consist of two hypotrocoids is not equal at each point of the cross section because of the character of hypotrocoids. Accordingly, we assume that the thickness of each element of the cross section is equal to it on the neutral axis. With this assumption, we can obtain an approximate solution for the shearing stress distribution of square-tube the wall thickness of which is equal at each point of the cross section. Further, the shapes of the cross section bounded by two hypotrocoids vary by the values of variable. Namely, square-tube becomes concentric circles by degrees. Then, we discuss the differences of shearing stress distributions by the variation of shapes of hollow cross sections. In consequence, we can find that in the case of square-tube the maximum value of shearing stress occurs at the outside of the boundary of the cross section on the neutral axis, and on the contrary in the case of concentric circles it occurs at the inside of the boundary of the cross section on the neutral axis.
